A homotopy-theoretic rigidity property of Bott manifolds
University of Aberdeen
The rigidity conjecture in toric topology posits that two toric
manifolds are diffeomorphic if and only if their integral cohomology
rings are isomorphic as graded rings. Only a few low dimensional
cases have been resolved. We weaken the conjecture to one concerning
homotopy type rather than diffeomorphism, and show that the
weaker conjecture holds for Bott manifolds, once enough primes
have been inverted. In particular, show that the rational homotopy
type of a Bott manifold is determined by its rational cohomology ring.
The material in this paper was inspired by the mathematics discussed at the International conference
«Toric Topology and Automorphic Functions» (September, 5–10th, 2011, Khabarovsk, Russia).
Bott manifold, rigidity.
PDF file (212 kB)
MSC: Primary 55P15; Secondary 57R19
S. Theriault, “A homotopy-theoretic rigidity property of Bott manifolds”, Dal'nevost. Mat. Zh., 12:1 (2012), 89–97
Citation in format AMSBIB
\paper A homotopy-theoretic rigidity property of Bott manifolds
\jour Dal'nevost. Mat. Zh.
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